Distance

Speed

Time

*These are all scalar quantities-only magnitude

Displacement

Velocity

Acceleration

*These are all vector quantities-magnitude and direction

DISTANCE

Total traveled Path dependent Scalar quantity

Both use the same variable and units Variable: d (sometimes:

x,r,ℓ) Units: m

DISPLACEMENT

Change in position Path independent Vector quantity

An odometer in your car shows:

Distance

The following is a list of gains and loses of a Bears possession First down: gain 8

yards Penalty lose 10 yards Second down: gain

11 yards Third down: lose 1

yard

What is the total distance?

What is the total displacement?

DIFFERENCES

Speed: how fast (scalar) Always positive Example: 25 m/s

Velocity: how fast in a certain direction (vector) Can be positive or

negative Example: 25 m/s North

SIMILARITIES

Variable: v Units: m/s

A speedometer in your car shows:

Speed

Jim travels from Palatine to Chicago at 65 mph. Susie travels from Chicago to Palatine at 65 mph. Are the velocities equal?

No, different directions

v=(df-di)/(tf-ti)OR commonly written as

v=∆d/ ∆ t

*∆ means change

Average Speed/Velocity

In gym, you have to run the 100 m dash. If you run it in 18 s, what was your velocity?

A freaky fast Jimmy Johns delivery man makes a delivery that is 2.2 miles away and it takes him 9 min. What is his average velocity in mi/hr?

SPEED (AVERAGE)

Total distance traveled divided by the total time elapsed

**Example: Round trip drive to school

VELOCITY

Total displacement divided by total time

A change in velocity Vector quantity Positive vs. Negative

Acceleration + velocity and + acceleration =

_____ + velocity and - acceleration =

_____ - velocity and - acceleration =

_____ - velocity and + acceleration =

_____

Variable: a Units: m/s/s or m/s2

Equation:a=(vf-vi)/(tf-ti)

OR commonly written as:

a= ∆v/ ∆ t

Name 3 ways to accelerate your car:1.Step on gas pedal2.Step on brake pedal3.Turn steering wheel

A car accelerates from a stop sign up to a speed of 11 m/s. If it takes 4 to do so, what is the car’s acceleration?

Problem 1: How long does it

take a turtle to travel 1,000 m if it can travel at a pace of 1.3 m/s?

Problems 2: What is the change

in velocity if an object accelerates at 2 m/s2 for 4.5 seconds?

If the object

started at 3 m/s, what is its final speed?

DISTANCE VS. TIME GRAPHSVELOCITY VS. TIME GRAPHS

Slope is acceleration Slope = rise/run =

velocity/time = ACCELERATION

Area under graph is distance traveled Area = base*height =

velocity*time = Distance

Slope is velocity Slope = rise/run =

distance/time = Velocity

Straight Lines – CONSTANTCurving Lines – CHANGINGFlat Line - ZERO

Steeper the slope, the higher the value

Definition of average velocity: (vi + vf)/2

Distance = rate * time: d=vavg*t

Definition of acceleration (final velocity): vf=vi + at

Timeless: vf

2=vi2 +2a∆d

Position: ∆d=vit +1/2at2

Equation ∆x vi vf ∆t a

Definition of average velocity: vavg=(vi + vf)/2

Distance = rate * time:x=vavg*t √ √ √ √ ○

Definition of acceleration (final velocity): vf=vi + at

○ √ √ √ √

Timeless:vf

2=vi2 +2a∆x √ √ √ ○ √

Position:∆x=vit +1/2at2 √ √ ○ √ √

Identify givens Look for hidden givens

Identify unknown(s)Compare givens and unknowns to

equations In the beginning: chart

Re-read problem if stuck

*always show your work (G.U.E.S.S.)

What is Starlin Castro’s acceleration as he runs toward first base if he reaches the base with a speed of 6.5 m/s? The distance between the plates is 27.432 meters .

An airplane can accelerate at a rate of 4.9m/s2. If it takes 45 s for the plane to start to elevate and the plane starts from rest, what is the minimum length of runway required?

Seeing a stop sign ahead, a person begins to brake as they drive lawfully on Cunningham. If their reaction time is 1 s, what is the total distance they need to stop if they can accelerate at -8 m/s2?